Question

assume (-2,0) and (3,0) are the x intercepts of y=f(x). find the x intercepts of g(x)= f(x-3)

Answer 1

The intercepts of a graph are the points the graph crosses the x-axis

The x-intercepts of $\mathbf{g(x) = f(x - 3)}$ are (-5,0) and (0,0)

For y = f(x), we have

$\mathbf{(x,y) = (-2,0)\ (3,0)}$

For g(x) = f(x - 3), we have:

$\mathbf{(x-3,y) = (-2-3,0)\ (3-3,0)}$

$\mathbf{(x-3,y) = (-5,0)\ (0,0)}$

Recall that:

$\mathbf{g(x) = f(x - 3)}$

Hence, the x-intercepts of $\mathbf{g(x) = f(x - 3)}$ are (-5,0) and (0,0)

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